Multiscale phonon transport simulations by a discrete ordinate method with streaming and collision processes

It is challenging to solve the phonon Boltzmann transport equation numerically due to the stiff collision term induced by small relaxation time. In this work, a discrete ordinate method with streaming and collision processes is developed for phonon Boltzmann transport equation. This method is explicit and does not need a linear solver. Moreover, it is uniformly stable in terms of the Knudsen number and has an asymptotic-preserving property. Thus, the time step is not restricted by the phonon relaxation time. In order to validate the present method, we investigate four numerical test cases, including cross-plane heat conduction, in-plane heat conduction, one-dimensional transient thermal grating problem and a hotspot problem. Numerical results show that the present method can capture the ballistic-diffusive transport phenomenon accurately and efficiently in a wide range of Knudsen numbers, and may provide an alternative tool for a deep research into multiscale phonon transport problem.